The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  X  0  1  1  1  X  1  0  1  X  0  1  1  0  1  1  1  X  1  1  1  X  X  0  0  1  1  1  1  1  2  2  1  X  X  1  0  1  1  X  1  1  0  1  X  0  1  1  1  1  1
 0  X  0 X+2  0 X+2  0 X+2  0 X+2  2 X+2  0 X+2  0 X+2  X  2 X+2  0  2 X+2  2  X X+2  X X+2 X+2  X  0  2  X X+2 X+2  X X+2 X+2  X  0  0  X  X  2  0 X+2  0  0 X+2 X+2 X+2  X  X  X  X  0  2  X  X  0  X X+2 X+2  2  X  0  0  X  0  2  X X+2  0  X X+2 X+2  0  0  0
 0  0  2  0  0  0  0  0  0  0  2  0  2  0  0  0  0  2  2  2  2  2  0  2  0  0  0  2  2  2  0  0  2  2  2  2  0  0  2  0  0  0  0  0  2  2  0  2  0  0  0  2  0  2  2  2  0  2  2  2  0  2  2  2  0  0  0  2  0  2  0  0  0  0  0  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  0  2  0  0  2  0  2  0  2  2  2  0  2  2  0  2  2  0  0  0  2  0  2  0  2  0  0  2  2  2  2  2  0  2  0  0  0  2  2  0  2  2  0  2  0  2  0  0  2  0  2  2  0  0  0  2  0  0  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  2  0  0  0  0  2  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  2  2  2  2  0  0  2  0  0  2  2  2  2  0  0  2  0  0  2  0  0  2  0  0  2  2  2  2  2  0  0  0  0  0  0  2  2  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  2  0  2  0  2  0  0  2  0  2  0  2  2  2  2  0  0  0  0  2  2  2  0  2  2  2  2  2  0  2  2  2  0  0  0  2  2  2  0  2  2  2  2  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  2  0  0  0  0  2  2  0  2  0  2  0  0  0  2  2  0  0  2  2  0  2  0  2  0  2  2  2  0  2  0  0  0  0  2  0  2  0  2  0  0  2  0  2  2  0  0  0  2  2  2  0  2  0  2  0  2  2  2  2  0  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  2  2  0  2  2  0  2  2  0  0  0  2  0  2  2  0  0  2  2  2  0  0  2  0  0  0  0  0  2  2  2  0  2  2  2  0  2  0  2  2  2  0  0  2  0  0  0  0  0  2  2  0  0  2  2  0  0  0  2  2  0  2  2  0
 0  0  0  0  0  0  0  0  2  0  2  0  2  0  2  2  2  0  2  0  2  0  0  2  2  0  2  2  0  0  0  2  2  0  2  0  2  0  0  2  2  0  0  0  2  2  2  0  0  2  2  0  0  0  2  2  0  0  0  2  2  2  2  0  0  0  0  2  0  2  2  0  0  2  2  0  0  0
 0  0  0  0  0  0  0  0  0  2  0  2  0  0  2  0  2  2  2  2  0  0  2  2  2  0  0  2  2  0  2  2  2  2  2  0  0  0  2  2  0  2  2  2  0  2  0  0  0  2  0  2  0  2  2  0  0  2  2  0  2  2  2  0  2  0  2  0  2  2  0  0  2  2  0  2  2  0

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+57x^64+57x^66+30x^67+140x^68+90x^69+188x^70+216x^71+267x^72+384x^73+422x^74+576x^75+634x^76+740x^77+654x^78+736x^79+568x^80+624x^81+422x^82+398x^83+261x^84+178x^85+194x^86+88x^87+75x^88+32x^89+59x^90+4x^91+36x^92+31x^94+8x^96+15x^98+1x^100+4x^102+1x^106+1x^110

The gray image is a code over GF(2) with n=312, k=13 and d=128.
This code was found by Heurico 1.16 in 8.47 seconds.